Computational Mechanics

, Volume 55, Issue 6, pp 1071–1078

Vibration of structures containing compressible liquids with surface tension and sloshing effects. Reduced-order model

Original Paper


This paper deals with the development of the linear vibration of a general viscoelastic structure, with a local wall acoustic impedance, containing an inviscid compressible liquid (but with an additional volume dissipative term), with surface tension (capillarity) and sloshing effects, and neglecting the effects of internal gravity waves and the elastogravity operator. The sloshing problems of incompressible liquids with capillarity effects in elastic structures exhibit a major difficulty induced by the boundary contact conditions on the triple line because the capillarity forces are forces per unit length while the elastic forces are forces per unit surface. The proposed framework has the following novel features: (i) introducing a new appropriate boundary condition for the contact angle condition compatible with a deformable structure considered here as viscoelastic, (ii) considering a compressible liquid while incompressibility hypothesis is generally used for FSI problems including capillarity phenomena, and (iii) constructing a reduced-order model for the computational coupled problem.


Linear vibration Viscoelastic structure Surface tension Sloshing Contact angle condition Reduced-order-model 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Structural Mechanics and Coupled Systems LaboratoryConservatoire National des Arts et Métiers (CNAM)ParisFrance
  2. 2.Modelisation et Simulation Multi-Echelle, MSME UMR 8208 CNRSUniversité Paris-EstMarne-la-Vallée Cedex 02France

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